Question

In a Fraunhofer diffraction at single slit of width d with incident light of wavelength 5500 $?$, the first minimum is observed, at angle 30$^{\circ}$. The first secondary maximum is observed at an angle $\theta$ =

• A. $sin^{-1} \frac{1}{\sqrt{2}}$
• B. $sin^{-1} \frac{1}{4}$
• C. $sin^{-1} \frac{3}{4}$
• D. $sin^{-1} \frac{\sqrt{3}}{2}$

Answer 1

The Correct Option is C

Slit width = d $\lambda = 5500 ? = 5.5 ? 10^{-7} m, \theta_{n} = 30^{\circ}$ For first secondary minima, d sin$\theta_{n} = \lambda$ $d=\frac{\lambda}{ sin\theta_{n}}=\frac{5.5\times10^{-7}}{sin 30^{\circ}}=11\times10^{-7}m$ For first secondary maxima, d sin $\theta_{n}=\frac{3\lambda}{2}$ i. e. sin $\theta_{n}=\frac{3\lambda}{2d}=\frac{3\times5.5\times10^{-7}}{2\times11\times10^{-7}}$ sin $\theta_{n}=\frac{3}{4}$ or $\theta_{n}=sin^{-1} \left(3/4\right)$